| Title:
|
On nonresonance impulsive functional nonconvex valued differential inclusions (English) |
| Author:
|
Benchohra, M. |
| Author:
|
Henderson, J. |
| Author:
|
Ntouyas, S. K. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
595-604 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces. (English) |
| Keyword:
|
impulsive functional differential inclusions |
| Keyword:
|
nonresonance problem |
| Keyword:
|
fixed \newline point |
| Keyword:
|
Banach space |
| MSC:
|
34A37 |
| MSC:
|
34A60 |
| MSC:
|
34G20 |
| MSC:
|
34G25 |
| MSC:
|
34K25 |
| MSC:
|
34K45 |
| idZBL:
|
Zbl 1090.34006 |
| idMR:
|
MR2045783 |
| . |
| Date available:
|
2009-01-08T19:25:32Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119350 |
| . |
| Reference:
|
[1] Bainov D.D., Simeonov P.S.: Systems with Impulse Effect.Ellis Horwood Ltd., Chichister, 1989. Zbl 0714.34083, MR 1010418 |
| Reference:
|
[2] Benchohra M., Eloe P.: On nonresonance impulsive functional differential equations with periodic boundary conditions.Appl. Math. E.-Notes 1 (2001), 65-72. Zbl 0983.34077, MR 1833839 |
| Reference:
|
[3] Benchohra MK., Henderson J., Ntouyas S.K.: On nonresonance impulsive functional differential inclusions with periodic boundary conditions.Intern. J. Appl. Math. 5 (4) (2001), 377-391. Zbl 1038.34083, MR 1852836 |
| Reference:
|
[4] Benchohra M., Henderson J., Ntouyas S.K.: On nonresonance second order impulsive functional differential inclusions with nonlinear boundary conditions.Canad. Appl. Math. Quart., in press. Zbl 1146.34055 |
| Reference:
|
[5] Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl 0346.46038, MR 0467310 |
| Reference:
|
[6] Covitz H., Nadler S.B., Jr.: Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8 (1970), 5-11. MR 0263062 |
| Reference:
|
[7] Deimling K.: Multivalued Differential Equations.Walter de Gruyter, Berlin-New York, 1992. Zbl 0820.34009, MR 1189795 |
| Reference:
|
[8] Dong Y.: Periodic boundary value problems for functional differential equations with impulses.J. Math. Anal. Appl. 210 (1997), 170-181. Zbl 0878.34059, MR 1449515 |
| Reference:
|
[9] Gorniewicz L.: Topological Fixed Point Theory of Multivalued Mappings.Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999. Zbl 1107.55001, MR 1748378 |
| Reference:
|
[10] Hu Sh., Papageorgiou N.: Handbook of Multivalued Analysis, Volume I: Theory.Kluwer Academic Publishers, Dordrecht, Boston, London, 1997. Zbl 0887.47001, MR 1485775 |
| Reference:
|
[11] Lakshmikantham V., Bainov D.D., Simeonov P.S.: Theory of Impulsive Differential Equations.World Scientific, Singapore, 1989. Zbl 0719.34002, MR 1082551 |
| Reference:
|
[12] Nieto J.J.: Basic theory for nonresonance impulsive periodic problems of first order.J. Math. Anal. Appl. 205 (1997), 423-433. Zbl 0870.34009, MR 1428357 |
| Reference:
|
[13] Samoilenko A.M., Perestyuk N.A.: Impulsive Differential Equations.World Scientific, Singapore, 1995. MR 1355787 |
| . |
